diff --git a/django/db/migrations/autodetector.py b/django/db/migrations/autodetector.py
index a6edc2cd6ef..89e2dceeaf8 100644
--- a/django/db/migrations/autodetector.py
+++ b/django/db/migrations/autodetector.py
@@ -9,9 +9,7 @@ from django.db.migrations.migration import Migration
 from django.db.migrations.operations.models import AlterModelOptions
 from django.db.migrations.optimizer import MigrationOptimizer
 from django.db.migrations.questioner import MigrationQuestioner
-from django.db.migrations.utils import (
-    COMPILED_REGEX_TYPE, RegexObject, get_migration_name_timestamp,
-)
+from django.db.migrations.utils import COMPILED_REGEX_TYPE, RegexObject
 from django.utils.topological_sort import stable_topological_sort
 
 
@@ -1265,13 +1263,14 @@ class MigrationAutodetector:
             for i, migration in enumerate(migrations):
                 if i == 0 and app_leaf:
                     migration.dependencies.append(app_leaf)
-                if i == 0 and not app_leaf:
-                    new_name = "0001_%s" % migration_name if migration_name else "0001_initial"
+                new_name_parts = ['%04i' % next_number]
+                if migration_name:
+                    new_name_parts.append(migration_name)
+                elif i == 0 and not app_leaf:
+                    new_name_parts.append('initial')
                 else:
-                    new_name = "%04i_%s" % (
-                        next_number,
-                        migration_name or self.suggest_name(migration.operations)[:100],
-                    )
+                    new_name_parts.append(migration.suggest_name()[:100])
+                new_name = '_'.join(new_name_parts)
                 name_map[(app_label, migration.name)] = (app_label, new_name)
                 next_number += 1
                 migration.name = new_name
@@ -1306,22 +1305,6 @@ class MigrationAutodetector:
                 del changes[app_label]
         return changes
 
-    @classmethod
-    def suggest_name(cls, ops):
-        """
-        Given a set of operations, suggest a name for the migration they might
-        represent. Names are not guaranteed to be unique, but put some effort
-        into the fallback name to avoid VCS conflicts if possible.
-        """
-        name = None
-        if len(ops) == 1:
-            name = ops[0].migration_name_fragment
-        elif len(ops) > 1 and all(isinstance(o, operations.CreateModel) for o in ops):
-            name = '_'.join(sorted(o.migration_name_fragment for o in ops))
-        if name is None:
-            name = 'auto_%s' % get_migration_name_timestamp()
-        return name
-
     @classmethod
     def parse_number(cls, name):
         """
diff --git a/django/db/migrations/migration.py b/django/db/migrations/migration.py
index fe5e228c6c5..08fdd1914fd 100644
--- a/django/db/migrations/migration.py
+++ b/django/db/migrations/migration.py
@@ -1,3 +1,5 @@
+from django.db.migrations import operations
+from django.db.migrations.utils import get_migration_name_timestamp
 from django.db.transaction import atomic
 
 from .exceptions import IrreversibleError
@@ -175,6 +177,24 @@ class Migration:
                 operation.database_backwards(self.app_label, schema_editor, from_state, to_state)
         return project_state
 
+    def suggest_name(self):
+        """
+        Suggest a name for the operations this migration might represent. Names
+        are not guaranteed to be unique, but put some effort into the fallback
+        name to avoid VCS conflicts if possible.
+        """
+        name = None
+        if len(self.operations) == 1:
+            name = self.operations[0].migration_name_fragment
+        elif (
+            len(self.operations) > 1 and
+            all(isinstance(o, operations.CreateModel) for o in self.operations)
+        ):
+            name = '_'.join(sorted(o.migration_name_fragment for o in self.operations))
+        if name is None:
+            name = 'auto_%s' % get_migration_name_timestamp()
+        return name
+
 
 class SwappableTuple(tuple):
     """
diff --git a/tests/migrations/test_autodetector.py b/tests/migrations/test_autodetector.py
index ab52b8116d6..dddda94eb26 100644
--- a/tests/migrations/test_autodetector.py
+++ b/tests/migrations/test_autodetector.py
@@ -2481,25 +2481,39 @@ class AutodetectorTests(TestCase):
         self.assertOperationAttributes(changes, 'app', 0, 1, name='book')
 
 
-class AutodetectorSuggestNameTests(SimpleTestCase):
+class MigrationSuggestNameTests(SimpleTestCase):
     def test_single_operation(self):
-        ops = [migrations.CreateModel('Person', fields=[])]
-        self.assertEqual(MigrationAutodetector.suggest_name(ops), 'person')
-        ops = [migrations.DeleteModel('Person')]
-        self.assertEqual(MigrationAutodetector.suggest_name(ops), 'delete_person')
+        class Migration(migrations.Migration):
+            operations = [migrations.CreateModel('Person', fields=[])]
+
+        migration = Migration('0001_initial', 'test_app')
+        self.assertEqual(migration.suggest_name(), 'person')
+
+        class Migration(migrations.Migration):
+            operations = [migrations.DeleteModel('Person')]
+
+        migration = Migration('0002_initial', 'test_app')
+        self.assertEqual(migration.suggest_name(), 'delete_person')
 
     def test_two_create_models(self):
-        ops = [
-            migrations.CreateModel('Person', fields=[]),
-            migrations.CreateModel('Animal', fields=[]),
-        ]
-        self.assertEqual(MigrationAutodetector.suggest_name(ops), 'animal_person')
+        class Migration(migrations.Migration):
+            operations = [
+                migrations.CreateModel('Person', fields=[]),
+                migrations.CreateModel('Animal', fields=[]),
+            ]
+
+        migration = Migration('0001_initial', 'test_app')
+        self.assertEqual(migration.suggest_name(), 'animal_person')
 
     def test_none_name(self):
-        ops = [migrations.RunSQL('SELECT 1 FROM person;')]
-        suggest_name = MigrationAutodetector.suggest_name(ops)
+        class Migration(migrations.Migration):
+            operations = [migrations.RunSQL('SELECT 1 FROM person;')]
+
+        migration = Migration('0001_initial', 'test_app')
+        suggest_name = migration.suggest_name()
         self.assertIs(suggest_name.startswith('auto_'), True)
 
     def test_auto(self):
-        suggest_name = MigrationAutodetector.suggest_name([])
+        migration = migrations.Migration('0001_initial', 'test_app')
+        suggest_name = migration.suggest_name()
         self.assertIs(suggest_name.startswith('auto_'), True)